7. Kevin can run a lap around the field in 4-6 minutes. If he has 30 minutes to run, how
many laps is he able to finish?
The number of laps that Kevin can run is 5 laps.
How to calculate the number of laps?From the information, Kevin can run a lap around the field in 4-6 minutes and he has 30 minutes to run.
Therefore, the number of laps that he can run will be:
= Total minutes / Time taken for each lap
= 30 minutes / 6
= 5 laps.
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A straight line has a gradient of 4 and passes through the point (2,9).
Work out the equation of the line.
Give your answer in the form y = mx + c, where m and c are integers or
fractions in their simplest forms.
The equation of the given line passes through the point (2,9) y = 4x + 1.
What exactly is the slope of a line?The slope of a line indicates its steepness. The slope is determined mathematically as "increase over run" (change in y divided by change in x).
A line equation is defined as:The conventional form of a line equation is ax + by + c = 0. Here, the coefficients are a and b, the variables are x and y, and the constant term is c. It is a one-degree equation with variables x and y. The coordinates of both the point on the line that appears in the coordinate plane are represented by the values of x and y.
According to the given data:m = 4
equation of the line = y = mx + c
substituting the value of m = 4
y = 4x + c
the point (2,9):
putting the points in the line of the equation:
x = 2
y = 9
So,
y = mx + c
9 = 4 * 2 + c
9 = 8 + c
c = 1
The equation of the given line y = 4x + 1.
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Answer:
y=4x+1
Step-by-step explanation:
y-y1=m(x-x1)
y-9=4(x-2)
y=4x-8+9
y=4x+1
aaliyah compares the heights of two plants to see which plant grows more per day. The table shows the height of Plant 1, in centimeters, over 5 days. The graph shows the height of Plant 2, in centimeters, over 10 days. aaliyah says that since Plant 1 grows 4cm per day and Plant 2 grows 6cm per day, plant 2 grows more per day. Do you agree with aaliyah? Explain your response.
A. I agree that plant 2 grows more per day than plant 1, but I disagree with aaliyahs's reasoning.
B.
I think that plant 1 grows more per day than plant 2, but I agree with aaliyah's reasoning.
C.
I think that plant 1 grows more per day than plant 2, and I disagree with aaliyahs's reasoning.
D.
I agree that plant 2 grows more per day than plant 1, and I agree with aaliyah's reasoning.
The table that shows the growth rate of Plant 1 which is 4 cm/week, and the graph that gives the growth rate of Plant 2 as 2 cm/week gives the correct option as C;
C. I think that plant 1 grows more per day and I disagree with Aaliyah's reasoning
What is a proportional relationship?A proportional relationship between two variables is one in which one variable is a multiple of the other.
The possible table in the question is presented as follows;
Plant 1
Week; 2, 3, 4, 5Height; 8, 12, 16, 20The values on the graph are;
Plant 2
Week; 2, 4, 6, 8, 10Height; 4, 8, 12, 16, 20The rate, r1, of growth of Plant 1 is therefore;
r1 = 8 cm/(2 weeks) = 4 cm/week
The rate, of growth, r2, of plant 2 is found as follows;
r2 = 4 cm/(2 weeks) = 2 cm/week
Given that Plant 1 grows faster at 4 cm/week, than Plant 2, that grows at 2 cm/week, the correct statement is since Plant 1 grows 4 cm/week and Plant 2 grows 2 cm/week, Plant 1 grows more per day.
The correct option is therefore;
C. I think that plant 1 grows more per day and I disagree with Aaliyah's reasoning
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A man owns 50 shares of stock worth $30 each. The corporation declared a dividend of 6% payable in stock. How many shares did he then own?
Answer:53 shares
Step-by-step explanation:
If we assume the price remained constant, then the number of shares increased by 6%.
(50 shares)(1 +6%) = 53 shares
The man then owned 53 shares
How many times greater is 70,000 than 7,000?
Answer
70.000 в 10 раз больше 7.000
Step-by-step explanation:
Name the geometric term modeled by the given object.
a telephone pole
The geometric term modeled by the given object (a telephone pole) is a line
How to determine the geometric term?The given object is a telephone pole
The pole of a telephone pole is often straight.
This means that the telephone pole can be modelled by a line segment
Hence, the geometric term modeled by the given object (a telephone pole) is a line
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andrew took a handful of change out of his picket adn noticed taht he was only holding dimes adn quarters in his hand. he counted that he had 22 coins that ammounted to $4. how many quarters and how many dimes does andrew have?
Andrew has 7 dimes and 15 quarters, as obtained from the system of linear equations so formed.
What is a system of linear equations?A system of linear equations is a set of two or more linear equations. Linear equations refer to the equations that involve two or more variables in the form of "ax + b".
Given:
Number of coins = 22; only dimes and quarters.Amount of coins = $4To find: Number of dimes and quarters.
Finding:
Now, 1 dime = 10 cents and 1 Quarter = 25 centsAlso, 100 cents = $1=> By unitary method, $4 = 4(100) = 400 cents
Let the number of dimes be d and number of quarters be q.Now, According to question, a system of linear equations follows:d + q = 22 (Number of coins) => d = 22 - q (eqn1)
and 10d + 25q = 400 (amount of coins)
=> 10 ( 22 - q ) + 25q = 400
=> 220 - 10q + 25q = 400
=> 15q = 400 - 220 = 180
=> q = 12, i.e., number of quarters = 22 upon the solving of this system of linear equations.
On substituting the value of q in eqn1, we get: d = 22 - 15 = 7, i.e., number of dimes = 7.
Hence, Andrew has 7 dimes and 15 quarters, as obtained from the system of linear equations so formed.
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Find the equation of a line parallel to 3x + 3y = 21 that passes through the point
(8,-2).
Answer:
awsome
Step-by-step explanation:
565
Evaluate the expression with its given values. 5 x − 2 y ; x = 2 , y = − 1
The value of the given expression (5 x − 2 y) = 12.
What is substituting method:The substitution technique is an algebraic approach for solving simultaneous linear equations. In this procedure, the value of one variable through one equation is substituted in the second equation, as the name implies.
What is the substitution technique formula?Three phases are involved in the substitution method: Solve one equation for one of the variables. Substitute (plug-in) this expression in the other equation as well as solve. Replace the value in the original equation to obtain the equivalent variable.
According to the given data:5 x − 2 y
x = 2;
y = -1;
substituting the value in the given equation:
5 x − 2 y
5(2) - 2(-1)
5(2) - (-2)
5(2) +2
10+2
12
The value of the given expression (5 x − 2 y) = 12
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It takes Mike 18 minutes to finish reading 4 pages of a book. How
long does it take for him to finish reading 30 pages?
Answer:
135 minutes
Step-by-step explanation:
18 divided by 4
4.5 pages per minute
4.5 times 30 = 135
Answer: 135 minutes
Step-by-step explanation: 18 times 30, then divide by 4
The graph shows the cost, c, in dollars of using a carpooling
service for d days. Which equation represents the cost of the carpooling service?
A c = = d
B c = 6d
C d = 6c
D c = 6
Answer: where is the graph?
suppose that a function f has domain (-2,2) and range (-3,5). what is the domain of the function f(2x)?
The domain of the function f(2x) is (-1, 1).
Given that a function f has domain (-2,2) and range (-3,5).
We need to determine the domain of the function f(2x).
To determine the domain of the function f(2x), we need to consider how the original domain (-2,2) is affected by the transformation of multiplying the input by 2.
When we multiply x by 2, it stretches or compresses the function horizontally.
In this case, multiplying by 2 will stretch the original domain by a factor of 1/2.
To find the new domain, we divide the original domain endpoints by 2:
New domain = (-2/2, 2/2) = (-1, 1)
Therefore, the domain of the function f(2x) is (-1, 1).
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25 ft
2 ft
24 ft
Is it impossible?
By applying the criterion of the law of cosine, the triangle presented in the picture is possible.
Is this triangle possible?
Herein we find an hypothetical triangles with all side lengths known. A criterion is using the law of cosine, a possible triangle has cosine values between - 1 and 1. Then, we proceed to check for each side:
cos A = - (a² - b² - c²) / (2 · b · c)
cos A = - (25² - 2² - 24²) / (2 · 2 · 24)
cos A = - 0.469
cos B = - (b² - a² - c²) / (2 · a · c)
cos B = - (2² - 25² - 24²) / (2 · 25 · 24)
cos B = 0.998
cos C = - (c² - a² - b²) / (2 · a · b)
cos C = - (24² - 25² - 2²) / (2 · 25 · 2)
cos C = 0.53
Since the law of cosine gives realistic results, then the triangle presented in the picture is possible.
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State the property that justifies the statement.
If x/3=-15, then x=-45.
The value of x will be -45 by the multiplicative property for the given expression x/3=-15.
What is an expression?The mathematical expression is the combination of numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also be used to denote the logical syntax's operation order and other properties.
The given expression is x/3=-15. The value of x will be calculated as below:-
x/3=-15.
x = -15 x 3
x = -45
Therefore, the value of x will be -45 by the multiplicative property.
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f(x) = x²
What is f(x) + f(x) + f(x)?
The result of the given expression f(x) + f(x) + f(x) = 3x².
What is defined as the quadratic function?A quadratic function is one of the following: f(x) = ax² + bx + c, where a, b, and c are positive integers and an is not equal to zero.
A parabola is a curve that represents the graph of a quadratic function. Parabolas can open up or down, and their "width" or "steepness" can vary, but they all share the identical basic "U" shape.A quadratic equation is defined in mathematics as an equation of degree 2, which means that the highest exponent of the this function is 2.As per the given question;
f(x) = x²
Now, we have to estimate the value of the function;
= f(x) + f(x) + f(x)
Substitute the value of f(x).
= x² + x² + x²
= 3x²
Thus, the value of the given function is found as 3x².
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Yo help please I need this done it's about rational or irrational numbers u have to figure out if it's either rat or irr. If it's rational then figure out if it is a integers. If it's a integers then figure out if it's a whole number if it is then figure out if it's a natural number. Here's the order of it. R I W N and if it's irr then it's just I
All the numbers have been analyzed for being rational and irrational .
For -1 :
It is a rational number = R
It is an integer = I
For 2 / 3:
It is a rational number = R
For - 4.8 :
It is a rational number = R
For 7:
It is a rational number = R
It is an integer = I
It is an whole number = W
It is a natural number = N
For - 32 / 95
It is a rational number = R
For - 20 / 4 = -5:
It is a rational number = R
It is an integer = I
For 0:
It is a rational number = R
It is an integer = I
It is an whole number = W
For - 7.34:
It is a rational number = R
For 7 / 1239:
It is a irrational number = I
For √5:
It is a irrational number = I
Therefore, all the numbers have been analyzed for being rational and irrational .
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Determine which sequences of transformations could be applied to the parent function, f(x) = x, to obtain the graph above. Reflect over the y-axis, vertically stretch by a factor of 2, and then shift up 6 units Shift left 3 units, reflect over the y-axis, and then vertically stretch by a factor of 2 Shift up 6 units, reflect over the x-axis, and then vertically stretch by a factor of 2 Shift left 2 units, reflect over the y-axis, and then vertically stretch by a factor of 6 Reflect over the x-axis, vertically stretch by a factor of 2, and then shift up 6 units Shift right 3 units, reflect over the y-axis, and then vertically stretch by a factor of 2
The sequence of transformations could be applied to the parent function, f(x) = x, to obtain the graph is E. Shift up 6 units, reflect over the x-axis, and then vertically stretch by a factor of 2.
What is transformation?It should be noted that transformation simply means the movement of an object from a position to another position.
In this case, the sequence of transformations could be applied to the parent function, f(x) = x, to obtain the graph is to shift up 6 units, reflect over the x-axis, and then vertically stretch by a factor of 2.
Therefore sequence of transformations could be applied to the parent function, f(x) = x, to obtain the graph is E. Shift up 6 units, reflect over the x-axis, and then vertically stretch by a factor of 2.
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1. f(3)=2x-5 (show work)
Answer:
The answer is 1
Step-by-step explanation:
On a graph, it would be at the plot point (3,1)
The mean exam score for the first group of twenty examinees applying for a security
job is 35.3 with a standard deviation of 3.6.
The mean exam score for the second group of twenty examinees is 34.1 with a
standard deviation of 0.5. Both distributions are close to symmetric in shape.
a. Use the mean and standard deviation to compare the scores of the two groups.
b. The minimum score required to get an in-person interview is 33. Which group
do you think has more people get in-person interviews?
The mean exam score of the first group is [tex]35.3[/tex]
The mean exam score for the second group is [tex]34.1[/tex]
but [tex]35.3[/tex] is greater than [tex]34.1[/tex]
Standard deviation of the first group is [tex]3.6[/tex]
Standard deviation of the second group is [tex]0.5[/tex]
but [tex]3.6[/tex] is greater than [tex]0.5[/tex].
(a) We can draw a conclusion that the score of the second group is more evenly distributed.
(b) The second group has more people get in - person interviews because [tex]3.6\geq 0.6[/tex], so the scores of the exam for the second group are all close to 34.1. On the contrary, the score of exams for the first group is extreme polarization.
Mean: The average of a group of variables is referred to as the mean in mathematics and statistics. There are several methods for calculating the mean, including simple arithmetic means (adding the numbers together and dividing the result by the number of observations), geometric means, and harmonic means.Standard deviation: The square root of the variance is used to calculate the standard deviation, a statistic that expresses how widely distributed a database is in relation to its mean.To learn more about mean and standard deviation, click on the link given below:
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Randy's swimming coach kept track of his average 50-meter lap times during the first 3 weeks of training. How much greater was the percent of change from Week 1 to Week 2 than from Week 2 to Week 3? Round to the nearest tenth of a percent.
The percent of the first change is greater by 2.36%.
Time in 1st week = 28.8 sec
Time in 2nd week = 27.6 sec
Time in 3rd week = 27.1 sec
∴ Change of time from week 1 to week 2 = (28.8 - 27.6) sec
= 1.2 sec
∴ Percent of change from week 1 to week 2 = [tex]\frac{time change}{1st week time} \times 100[/tex] %
= [tex]\frac{1.2}{28.8} \times 100[/tex] %
= 4.17%
∴ Change of time from week 2 to week 3 = (27.6 - 27.1) sec
= 0.5 sec
∴ Percent of change from week 2 to week 3 = [tex]\frac{Time change}{2nd week time} \times 100[/tex] %
= [tex]\frac{0.5}{27.6} \times 100[/tex] %
= 1.81%
∴ The greater change was in the first week. The amount by which it was greater is = (4.17 - 1.81) %
= 2.36%
Answer) The percent of the first change is greater by 2.36%.
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8+3a+7b-5+2a-7b combine like terms means to add the coefficients (numbers) in front of like variables
Evaluate the expression when a = 7 and c= -3.
-a+4c
Hello,
[tex] - a + 4c = - 7 + 4 \times ( - 3) = - 7 - 12 =- 19[/tex]
Answer:
-19
Step-by-step explanation:
-7 + 4(-3)
-7 - 12= -19
Rosa ran the hurdles in 58.32 seconds. maya ran the hurdles in 54.078 seconds. what is the difference between the two times? 3.954 seconds 4.242 seconds 4.258 seconds 5.758 seconds
Answer:
Step-by-step explanation: 4.242
The difference of time taken by Rosa and Maya to ran the hurdles is 4.242 seconds .
The correct option is B .
Given, time taken by Rosa and Maya to ran the hurdles.
Time taken by Rosa to ran the hurdle = 58.32 seconds .
Time taken by Maya to ran the hurdle = 54.078 seconds .
Difference between the time taken:
Rosa is taking more time to cover the distance than Maya . Thus the speed of Rosa is less than the speed of Maya .
Relationship between speed, time and distance.
Distance = Speed × Time
Subtract time taken by Rosa to ran the hurdle from time taken by Maya to ran the hurdle.
= 58.32 - 54.078
= 4.242 seconds
Therefore the correct option is B .
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What is the image point of (8, -3) after a translation right 5 units and down 5 units?
which is the midpoint of AB?
Please help I’ll give Brainliest answer to whoever is correct
. Tell whether (7,-4) is a solution of y ≥ 5 - x.
(7,-4) is not a solution of the inequality y ≥ 5 - x
How to tell whether (7,-4) is a solution of y ≥ 5 - x?The inequality expression is given as
y ≥ 5 - x
The solution is given as:
(7, -4)
This means that
(x, y) = (7, -4)
Substitute (x, y) = (7, -4) in the inequality y ≥ 5 - x
So, we have
-4 ≥ 5 - 7
Evaluate the difference
-4 ≥ -2
On the numbering system, -4 is less than -2
Hence, (7,-4) is not a solution of the inequality y ≥ 5 - x
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Andrea, Roberto, Charlene, Maria, and Nguyen volunteer their time as computer science tutors after school. Due to their
schedules, though, they are only able to tutor on certain school days:
Andrea is able to tutor every second school day (every other school day).
Roberto is able to tutor every third school day.
Charlene is able to tutor every fourth school day.
Maria is able to tutor every sixth school day.
Nguyen is able to tutor every ninth school day.
If all five people are tutoring together today, how many school days from today will be the next time all five tutor together again?
From today 36 days later, all five will be tutoring again.
As we have given that,
Andrea is able to tutor every second school day
Roberto is able to tutor every third school day.
Charlene is able to tutor every fourth school day.
Maria is able to tutor every sixth school day.
Nguyen is able to tutor every ninth school day.
So, as a result, our working days are 2, 3, 4, 6, and 9 days.
Today's tutoring session will involve all five participants.
Next time, all five tutors will work together = LCM (2, 3, 4, 6, 9) = 36
Therefore, from today 36 days later, all five will be tutoring again.
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what is the answer to 3(x-2) = 6
[tex]3(x - 2) = 6 \\ x - 2 = \frac{6}{3} \\ x - 2 = 2 \\ x = 2 + 2 \\ x = 4[/tex]
Answer:
Step-by-step explanation:
x =4
5 1-3a
Note: Please make sure to properly format your answers. All dollar figures in the answers need to include the dollar sign and any amount over 1,000 should include the comma
($2,354.67). All percentage values in the answers need to include a percentage sign (%). For all items without specific rounding instructions, round your answers to two decimal
places, show both decimal places (5.06).
The variance of a distribution is 195. What is the standard deviation, rounded to the nearest thousandth?
Applying the square root of the variance, the standard deviation of the distribution is of 13.964.
What is the standard deviation of a distribution?The standard deviation of a distribution is given by the square root of the variance of the distribution.
For this problem, the variance of the distribution is of 195, hence the standard deviation is:
s = sqrt(195) = 13.964.
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Dwayne can spend no more than $12 at the grocery store buying loaves of bread and eggs. Each egg costs $0.20 and each loaf of
needs at least 6 eggs and 3 loaves of bread.
Let x represent the loaves of bread and y represent the number of eggs. Select all the inequalities that represent constraints for the situation.
OA 2x+0.2y>_ 9
OB. 2x+0.2y≤ 12
O C. x>_3
OD. x+y ≤ 12
O E x ≤ 3
OF. y ≤ 6
OG y>_6
The inequalities that represent constraints for the situation will be:
x+y ≤ 12
x >= 3
y >= 6
How to calculate the value?Let x represent the loaves of bread
Let y represent the number of eggs.
From the information, Each egg costs $0.20 and each loaf of needs at least 6 eggs and 3 loaves of bread.
Therefore,
x >= 3
>= 3y >= 6
Also, Dwayne can spend no more than $12 at the grocery store buying loaves of bread and eggs. This will be x+y ≤ 12.
The correct options are C, D, and F.
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